I believe so, is there a reason for it to remain on when it is not in use?
Not that I can think of. Save a bit of power, too.
I'm an energy conservation freak that unplugs every wall wart in my superinsulated shop when it's not in use, but realize I'm an anomaly in this world. Glad to hear someone else is thinking that way, even though it may be for different reasons.
Offhand, it seems a relay with electrical interlock supplying power to the VFD could work. The relay could be activated with a momentary switch and after the timed event has happened, turned off by the VFD itself. If I'm thinking of this correctly, the VFD would need an auxiliary input for the timer and an auxiliary NC output to control the relay.
Of course, simpler to just cut power to the VFD with a timed relay, IF the VFD could withstand it safely.
My apologies if this has already been suggested - I haven't read the thread completely.